TSTP Solution File: SYO500^1.003 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO500^1.003 : TPTP v7.5.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Mar 29 00:51:56 EDT 2022
% Result : Timeout 288.27s 288.66s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO500^1.003 : TPTP v7.5.0. Released v4.1.0.
% 0.12/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.33 % Computer : n015.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % RAMPerCPU : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Sun Mar 13 11:49:35 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.19/0.34 Python 2.7.5
% 5.08/5.24 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 5.08/5.24 FOF formula (<kernel.Constant object at 0xf945f0>, <kernel.Sort object at 0x2b3fe18f55a8>) of role type named x
% 5.08/5.24 Using role type
% 5.08/5.24 Declaring x:Prop
% 5.08/5.24 FOF formula (<kernel.Constant object at 0xf94e18>, <kernel.DependentProduct object at 0xf94b48>) of role type named f0
% 5.08/5.24 Using role type
% 5.08/5.24 Declaring f0:(Prop->Prop)
% 5.08/5.24 FOF formula (<kernel.Constant object at 0xf94ab8>, <kernel.DependentProduct object at 0xfb70e0>) of role type named f1
% 5.08/5.24 Using role type
% 5.08/5.24 Declaring f1:(Prop->Prop)
% 5.08/5.24 FOF formula (<kernel.Constant object at 0xf94b48>, <kernel.DependentProduct object at 0xfb7e18>) of role type named f2
% 5.08/5.24 Using role type
% 5.08/5.24 Declaring f2:(Prop->Prop)
% 5.08/5.24 FOF formula (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) of role conjecture named kaminski3
% 5.08/5.24 Conjecture to prove = (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))):Prop
% 5.08/5.24 We need to prove ['(((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))']
% 5.08/5.24 Parameter x:Prop.
% 5.08/5.24 Parameter f0:(Prop->Prop).
% 5.08/5.24 Parameter f1:(Prop->Prop).
% 5.08/5.24 Parameter f2:(Prop->Prop).
% 5.08/5.24 Trying to prove (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 5.08/5.24 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 x)))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) (f0 (f1 (f1 (f1 (f2 x))))))
% 5.08/5.24 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b)
% 5.08/5.24 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b)
% 5.08/5.24 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b)
% 5.08/5.24 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b)
% 5.08/5.24 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 5.08/5.24 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 5.08/5.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 5.08/5.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 5.08/5.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 5.08/5.24 Found x01:(P (f0 (f1 (f1 (f1 (f2 x))))))
% 5.08/5.24 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 x))))))
% 5.08/5.24 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 x))))))
% 5.08/5.24 Found x01:(P (f0 (f1 (f1 (f1 (f2 x))))))
% 5.08/5.24 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 x))))))
% 5.08/5.24 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P0 ((P (f0 (f1 (f1 (f1 (f2 x))))))->(P (f0 (f1 (f1 (f1 (f2 x))))))))
% 5.08/5.24 Found x01:(P (f0 (f1 (f1 (f1 (f2 x))))))
% 5.08/5.24 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 x))))))
% 5.08/5.24 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 x)))))
% 5.08/5.24 Found x01:(P (f0 (f1 (f1 (f1 (f2 x))))))
% 5.08/5.24 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 x))))))
% 5.08/5.24 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 x))))))
% 5.08/5.24 Found x01:(P (f0 (f1 (f1 (f1 (f2 x))))))
% 5.08/5.24 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 x))))))
% 5.08/5.24 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 x)))))))
% 5.08/5.24 Found x01:(P (f0 (f1 (f1 (f1 (f2 x))))))
% 5.08/5.24 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 x))))))
% 5.08/5.24 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 x)))))))
% 5.08/5.24 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 5.08/5.24 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 5.08/5.24 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 5.08/5.24 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 16.86/17.02 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 16.86/17.02 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 16.86/17.02 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 16.86/17.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 16.86/17.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 16.86/17.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 16.86/17.02 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 16.86/17.02 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 16.86/17.02 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 16.86/17.02 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 16.86/17.02 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 16.86/17.02 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 16.86/17.02 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 16.86/17.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 16.86/17.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 16.86/17.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 16.86/17.02 Found x01:(P (f1 (f1 (f1 (f2 x)))))
% 16.86/17.02 Found (fun (x01:(P (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P (f1 (f1 (f1 (f2 x)))))
% 16.86/17.02 Found (fun (x01:(P (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 x)))))
% 16.86/17.02 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 16.86/17.02 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 16.86/17.02 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P0 ((P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))->(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))))
% 16.86/17.02 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 16.86/17.02 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 16.86/17.02 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 16.86/17.02 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 16.86/17.02 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 16.86/17.02 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 16.86/17.02 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 16.86/17.02 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 16.86/17.02 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P0 (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))
% 16.86/17.02 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 16.86/17.02 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 16.86/17.02 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P0 (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))
% 16.86/17.02 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 16.86/17.02 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 16.86/17.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 16.86/17.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 16.86/17.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 16.86/17.02 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 16.86/17.02 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 16.86/17.02 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 16.86/17.02 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 16.86/17.02 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 16.86/17.02 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 23.64/23.82 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 23.64/23.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 23.64/23.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 23.64/23.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 23.64/23.82 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 23.64/23.82 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 23.64/23.82 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 23.64/23.82 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 23.64/23.82 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 23.64/23.82 Found x01:(P (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 23.64/23.82 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 23.64/23.82 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 23.64/23.82 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 x)))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) (f0 (f1 (f1 (f1 (f2 x))))))
% 23.64/23.82 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (P (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) (f0 (f1 (f1 (f1 (f2 x)))))))
% 23.64/23.82 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (P (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) (f0 (f1 (f1 (f1 (f2 x)))))))
% 23.64/23.82 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (P (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) (f0 (f1 (f1 (f1 (f2 x)))))))
% 23.64/23.82 Found x0:(P (f0 (f1 (f1 (f1 (f2 x))))))
% 23.64/23.82 Instantiate: b:=(f0 (f1 (f1 (f1 (f2 x))))):Prop
% 23.64/23.82 Found x0 as proof of (P0 b)
% 23.64/23.82 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 23.64/23.82 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 23.64/23.82 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 23.64/23.82 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 23.64/23.82 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 23.64/23.82 Found x0:(P0 (f0 (f1 (f1 (f1 (f2 x))))))
% 23.64/23.82 Found (fun (x0:(P0 (f0 (f1 (f1 (f1 (f2 x)))))))=> x0) as proof of (P0 (f0 (f1 (f1 (f1 (f2 x))))))
% 23.64/23.82 Found (fun (P0:(Prop->Prop)) (x0:(P0 (f0 (f1 (f1 (f1 (f2 x)))))))=> x0) as proof of ((P0 (f0 (f1 (f1 (f1 (f2 x))))))->(P0 (f0 (f1 (f1 (f1 (f2 x)))))))
% 23.64/23.82 Found (fun (P0:(Prop->Prop)) (x0:(P0 (f0 (f1 (f1 (f1 (f2 x)))))))=> x0) as proof of (P (f1 (f1 (f1 (f2 x)))))
% 23.64/23.82 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 x)))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) (f0 (f1 (f1 (f1 (f2 x))))))
% 23.64/23.82 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b)
% 23.64/23.82 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b)
% 23.64/23.82 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b)
% 23.64/23.82 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b)
% 23.64/23.82 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 23.64/23.82 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 23.64/23.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 23.64/23.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 23.64/23.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 23.64/23.82 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 23.64/23.82 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 23.64/23.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 23.64/23.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 23.64/23.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 30.18/30.37 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 30.18/30.37 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 30.18/30.37 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 30.18/30.37 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 30.18/30.37 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 30.18/30.37 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 30.18/30.37 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (P (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))
% 30.18/30.37 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (P (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))
% 30.18/30.37 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (P (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))
% 30.18/30.37 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 30.18/30.37 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 30.18/30.37 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 30.18/30.37 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 30.18/30.37 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 30.18/30.37 Found x0:(P0 b)
% 30.18/30.37 Instantiate: b:=(f0 (f1 (f1 (f1 (f2 x))))):Prop
% 30.18/30.37 Found (fun (x0:(P0 b))=> x0) as proof of (P0 (f0 (f1 (f1 (f1 (f2 x))))))
% 30.18/30.37 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (f0 (f1 (f1 (f1 (f2 x)))))))
% 30.18/30.37 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 30.18/30.37 Found x0:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 30.18/30.37 Instantiate: b:=(f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):Prop
% 30.18/30.37 Found x0 as proof of (P0 b)
% 30.18/30.37 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 x)))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) (f0 (f1 (f1 (f1 (f2 x))))))
% 30.18/30.37 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b)
% 30.18/30.37 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b)
% 30.18/30.37 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b)
% 30.18/30.37 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b)
% 30.18/30.37 Found x02:(P (f0 (f1 (f1 (f1 (f2 x))))))
% 30.18/30.37 Found (fun (x02:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x02) as proof of (P (f0 (f1 (f1 (f1 (f2 x))))))
% 30.18/30.37 Found (fun (x02:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x02) as proof of (P0 (f0 (f1 (f1 (f1 (f2 x))))))
% 30.18/30.37 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 x)))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) (f0 (f1 (f1 (f1 (f2 x))))))
% 30.18/30.37 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b)
% 30.18/30.37 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b)
% 30.18/30.37 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b)
% 30.18/30.37 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b)
% 30.18/30.37 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 30.18/30.37 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 30.18/30.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 30.18/30.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 30.18/30.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 30.18/30.37 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 x)))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) (f0 (f1 (f1 (f1 (f2 x))))))
% 30.18/30.37 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b0)
% 34.95/35.11 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b0)
% 34.95/35.11 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b0)
% 34.95/35.11 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b0)
% 34.95/35.11 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 34.95/35.11 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 34.95/35.11 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 34.95/35.11 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 34.95/35.11 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 34.95/35.11 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 34.95/35.11 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 34.95/35.11 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 34.95/35.11 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 34.95/35.11 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 34.95/35.11 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 34.95/35.11 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 34.95/35.11 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 34.95/35.11 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 34.95/35.11 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 34.95/35.11 Found x01:(P (f1 (f1 (f1 (f2 x)))))
% 34.95/35.11 Found (fun (x01:(P (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P (f1 (f1 (f1 (f2 x)))))
% 34.95/35.11 Found (fun (x01:(P (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 x)))))
% 34.95/35.11 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 34.95/35.11 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 34.95/35.11 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 34.95/35.11 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 34.95/35.11 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 34.95/35.11 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 34.95/35.11 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 34.95/35.11 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 34.95/35.11 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 34.95/35.11 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 34.95/35.11 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 34.95/35.11 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 34.95/35.11 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 34.95/35.11 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 34.95/35.11 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 34.95/35.11 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 34.95/35.11 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 34.95/35.11 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 34.95/35.11 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 34.95/35.11 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 34.95/35.11 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 34.95/35.11 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 34.95/35.11 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 48.76/48.94 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 48.76/48.94 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 48.76/48.94 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 48.76/48.94 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 48.76/48.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 48.76/48.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 48.76/48.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 48.76/48.94 Found x0:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 48.76/48.94 Found (fun (x0:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x0) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 48.76/48.94 Found (fun (P0:(Prop->Prop)) (x0:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x0) as proof of ((P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))->(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))
% 48.76/48.94 Found (fun (P0:(Prop->Prop)) (x0:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x0) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 48.76/48.94 Found x01:(P b)
% 48.76/48.94 Found (fun (x01:(P b))=> x01) as proof of (P b)
% 48.76/48.94 Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% 48.76/48.94 Found x0:(P (f0 (f1 (f1 (f1 (f2 x))))))
% 48.76/48.94 Instantiate: a:=(f1 (f1 (f1 (f2 x)))):Prop
% 48.76/48.94 Found x0 as proof of (P0 (P (f0 a)))
% 48.76/48.94 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 48.76/48.94 Found (eq_ref0 a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 48.76/48.94 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 48.76/48.94 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 48.76/48.94 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 48.76/48.94 Found x0:(P (f0 (f1 (f1 (f1 (f2 x))))))
% 48.76/48.94 Instantiate: a:=(f1 (f1 (f1 (f2 x)))):Prop
% 48.76/48.94 Found x0 as proof of (P0 a)
% 48.76/48.94 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 48.76/48.94 Found (eq_ref0 a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 48.76/48.94 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 48.76/48.94 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 48.76/48.94 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 48.76/48.94 Found x0:(P (f0 (f1 (f1 (f1 (f2 x))))))
% 48.76/48.94 Instantiate: a:=(f1 (f1 (f1 (f2 x)))):Prop
% 48.76/48.94 Found x0 as proof of (P0 (f0 a))
% 48.76/48.94 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 48.76/48.94 Found (eq_ref0 a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 48.76/48.94 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 48.76/48.94 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 48.76/48.94 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 48.76/48.94 Found x0:(P (f1 (f1 (f1 (f2 x)))))
% 48.76/48.94 Instantiate: b:=(f1 (f1 (f1 (f2 x)))):Prop
% 48.76/48.94 Found x0 as proof of (P0 b)
% 48.76/48.94 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 48.76/48.94 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 48.76/48.94 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 48.76/48.94 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 48.76/48.94 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 48.76/48.94 Found x02:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 48.76/48.94 Found (fun (x02:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x02) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 48.76/48.94 Found (fun (x02:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x02) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 48.76/48.94 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 48.76/48.94 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 48.76/48.94 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 53.65/53.83 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 53.65/53.83 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 53.65/53.83 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 53.65/53.83 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 53.65/53.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 53.65/53.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 53.65/53.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 53.65/53.83 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 53.65/53.83 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 53.65/53.83 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 53.65/53.83 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 53.65/53.83 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 53.65/53.83 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 53.65/53.83 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 53.65/53.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 53.65/53.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 53.65/53.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 53.65/53.83 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 53.65/53.83 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 53.65/53.83 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 53.65/53.83 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 53.65/53.83 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 53.65/53.83 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 53.65/53.83 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 53.65/53.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 53.65/53.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 53.65/53.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 53.65/53.83 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 53.65/53.83 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 53.65/53.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 53.65/53.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 53.65/53.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 53.65/53.83 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 53.65/53.83 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 53.65/53.83 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 53.65/53.83 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 53.65/53.83 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 53.65/53.83 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 53.65/53.83 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 53.65/53.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 53.65/53.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 53.65/53.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 53.65/53.83 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 53.65/53.83 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 53.65/53.83 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 53.65/53.83 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 53.65/53.83 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 53.65/53.83 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 54.86/55.07 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 54.86/55.07 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 54.86/55.07 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 54.86/55.07 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 54.86/55.07 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 54.86/55.07 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 54.86/55.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 54.86/55.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 54.86/55.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 54.86/55.07 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 54.86/55.07 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 54.86/55.07 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 54.86/55.07 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 54.86/55.07 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 54.86/55.07 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 54.86/55.07 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 54.86/55.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 54.86/55.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 54.86/55.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 54.86/55.07 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 54.86/55.07 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 54.86/55.07 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 54.86/55.07 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 54.86/55.07 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 54.86/55.07 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 54.86/55.07 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 54.86/55.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 54.86/55.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 54.86/55.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 54.86/55.07 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 54.86/55.07 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 54.86/55.07 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 54.86/55.07 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 54.86/55.07 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 54.86/55.07 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 54.86/55.07 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 54.86/55.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 54.86/55.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 54.86/55.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 54.86/55.07 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 54.86/55.07 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 54.86/55.07 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 54.86/55.07 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 54.86/55.07 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 54.86/55.07 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 54.86/55.07 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 54.86/55.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 54.86/55.07 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 59.50/59.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 59.50/59.69 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 59.50/59.69 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 59.50/59.69 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 59.50/59.69 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 59.50/59.69 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 59.50/59.69 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 59.50/59.69 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 59.50/59.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 59.50/59.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 59.50/59.69 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 59.50/59.69 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 59.50/59.69 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 x))))))
% 59.50/59.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 x))))))
% 59.50/59.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 x))))))
% 59.50/59.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f1 (f1 (f1 (f2 x))))))
% 59.50/59.69 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 59.50/59.69 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b0)
% 59.50/59.69 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b0)
% 59.50/59.69 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b0)
% 59.50/59.69 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b0)
% 59.50/59.69 Found x0:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 59.52/59.69 Instantiate: a:=(f0 (f0 (f1 (f2 (f2 (f2 x)))))):Prop
% 59.52/59.69 Found x0 as proof of (P0 (P (f0 a)))
% 59.52/59.69 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 59.52/59.69 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 x)))))
% 59.52/59.69 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 x)))))
% 59.52/59.69 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 x)))))
% 59.52/59.69 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 x)))))
% 59.52/59.69 Found x0:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 59.52/59.69 Instantiate: a:=(f0 (f0 (f1 (f2 (f2 (f2 x)))))):Prop
% 59.52/59.69 Found x0 as proof of (P0 (f0 a))
% 59.52/59.69 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 59.52/59.69 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 x)))))
% 59.52/59.69 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 x)))))
% 59.52/59.69 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 x)))))
% 59.52/59.69 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 x)))))
% 59.52/59.69 Found x0:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 59.52/59.69 Instantiate: a:=(f0 (f0 (f1 (f2 (f2 (f2 x)))))):Prop
% 59.52/59.69 Found x0 as proof of (P0 a)
% 59.52/59.69 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 59.52/59.69 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 x)))))
% 59.52/59.69 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 x)))))
% 59.52/59.69 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 x)))))
% 59.52/59.69 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f1 (f2 x)))))
% 59.52/59.69 Found x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 59.52/59.69 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 59.52/59.69 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P2 ((P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))->(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))))
% 59.52/59.69 Found x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 59.52/59.69 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 59.52/59.69 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P2 ((P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))->(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))))
% 62.60/62.78 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 62.60/62.78 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 62.60/62.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 62.60/62.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 62.60/62.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 62.60/62.78 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 62.60/62.78 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 62.60/62.78 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 62.60/62.78 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 62.60/62.78 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 62.60/62.78 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 62.60/62.78 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b0)
% 62.60/62.78 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b0)
% 62.60/62.78 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b0)
% 62.60/62.78 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b0)
% 62.60/62.78 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 62.60/62.78 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 62.60/62.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 62.60/62.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 62.60/62.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 62.60/62.78 Found x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 62.60/62.78 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 62.60/62.78 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 62.60/62.78 Found x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 62.60/62.78 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 62.60/62.78 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 62.60/62.78 Found x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 62.60/62.78 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 62.60/62.78 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P2 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 62.60/62.78 Found x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 62.60/62.78 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 62.60/62.78 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P2 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 62.60/62.78 Found x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 62.60/62.78 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 62.60/62.78 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P2 (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))
% 62.60/62.78 Found x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 62.60/62.78 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 62.60/62.78 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P2 (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))
% 62.60/62.78 Found x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 62.60/62.78 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 62.60/62.78 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P2 (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))
% 62.60/62.78 Found x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 62.60/62.78 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 62.60/62.78 Found (fun (x01:(P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P2 (P1 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))
% 68.18/68.36 Found x01:(P1 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found x01:(P1 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 68.18/68.36 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 68.18/68.36 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 68.18/68.36 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 68.18/68.36 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 68.18/68.36 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 68.18/68.36 Found x01:(P1 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found x01:(P1 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found x01:(P1 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found x01:(P1 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found x01:(P1 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found x01:(P1 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found x01:(P1 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found (fun (x01:(P1 (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P2 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found x01:(P (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 68.18/68.36 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 68.18/68.36 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 68.18/68.36 Found x02:(P (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found (fun (x02:(P (f1 (f1 (f1 (f2 x))))))=> x02) as proof of (P (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found (fun (x02:(P (f1 (f1 (f1 (f2 x))))))=> x02) as proof of (P0 (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 68.18/68.36 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 68.18/68.36 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 68.18/68.36 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 68.18/68.36 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 68.18/68.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 68.18/68.36 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 68.18/68.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 77.10/77.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 77.10/77.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 77.10/77.36 Found x01:(P b)
% 77.10/77.36 Found (fun (x01:(P b))=> x01) as proof of (P b)
% 77.10/77.36 Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% 77.10/77.36 Found x0:(P (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 77.10/77.36 Instantiate: b:=(f0 (f0 (f1 (f2 (f2 (f2 x)))))):Prop
% 77.10/77.36 Found x0 as proof of (P0 b)
% 77.10/77.36 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 77.10/77.36 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 77.10/77.36 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 77.10/77.36 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 77.10/77.36 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 77.10/77.36 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 77.10/77.37 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 77.10/77.37 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 77.10/77.37 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 77.10/77.37 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 77.10/77.37 Found x0:(P0 b)
% 77.10/77.37 Instantiate: b:=(f1 (f1 (f1 (f2 x)))):Prop
% 77.10/77.37 Found (fun (x0:(P0 b))=> x0) as proof of (P0 (f1 (f1 (f1 (f2 x)))))
% 77.10/77.37 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (f1 (f1 (f1 (f2 x))))))
% 77.10/77.37 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 77.10/77.37 Found x0:(P (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 77.10/77.37 Instantiate: b:=(f0 (f0 (f1 (f2 (f2 (f2 x)))))):Prop
% 77.10/77.37 Found x0 as proof of (P0 b)
% 77.10/77.37 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 77.10/77.37 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 77.10/77.37 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 77.10/77.37 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 77.10/77.37 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 77.10/77.37 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 x)))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) (f0 (f1 (f1 (f1 (f2 x))))))
% 77.10/77.37 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b)
% 77.10/77.37 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b)
% 77.10/77.37 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b)
% 77.10/77.37 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b)
% 77.10/77.37 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 77.10/77.37 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 77.10/77.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 77.10/77.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 77.10/77.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 77.10/77.37 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 77.10/77.37 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b0)
% 77.10/77.37 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b0)
% 77.10/77.37 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b0)
% 77.10/77.37 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b0)
% 77.10/77.37 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 77.10/77.37 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 77.10/77.37 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 77.10/77.37 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 104.98/105.21 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 104.98/105.21 Found x01:(P (f0 (f1 (f1 (f1 (f2 x))))))
% 104.98/105.21 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 x))))))
% 104.98/105.21 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 x))))))
% 104.98/105.21 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 104.98/105.21 Found (eq_ref0 a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 x))))))
% 104.98/105.21 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 x))))))
% 104.98/105.21 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 x))))))
% 104.98/105.21 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 x))))))
% 104.98/105.21 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 104.98/105.21 Found (eq_ref0 a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 x))))))
% 104.98/105.21 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 x))))))
% 104.98/105.21 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 x))))))
% 104.98/105.21 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 x))))))
% 104.98/105.21 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 104.98/105.21 Found (eq_ref0 a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 x))))))
% 104.98/105.21 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 x))))))
% 104.98/105.21 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 x))))))
% 104.98/105.21 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 x))))))
% 104.98/105.21 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 104.98/105.21 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 104.98/105.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 104.98/105.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 104.98/105.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 104.98/105.21 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 104.98/105.21 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 104.98/105.21 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 104.98/105.21 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 104.98/105.21 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 104.98/105.21 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 104.98/105.21 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 104.98/105.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 104.98/105.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 104.98/105.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 104.98/105.21 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 104.98/105.21 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 104.98/105.21 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 104.98/105.21 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 104.98/105.21 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 104.98/105.21 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 104.98/105.21 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 104.98/105.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 104.98/105.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 104.98/105.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 104.98/105.21 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 104.98/105.21 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 104.98/105.21 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 104.98/105.21 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 104.98/105.21 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 110.80/111.09 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 110.80/111.09 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 110.80/111.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 110.80/111.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 110.80/111.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 110.80/111.09 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 110.80/111.09 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 110.80/111.09 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 110.80/111.09 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 110.80/111.09 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 110.80/111.09 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 110.80/111.09 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 110.80/111.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 110.80/111.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 110.80/111.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 110.80/111.09 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 110.80/111.09 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 110.80/111.09 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 110.80/111.09 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 110.80/111.09 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 110.80/111.09 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 110.80/111.09 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 110.80/111.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 110.80/111.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 110.80/111.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 110.80/111.09 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 110.80/111.09 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 110.80/111.09 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 110.80/111.09 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 110.80/111.09 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 110.80/111.09 Found x01:(P b)
% 110.80/111.09 Found (fun (x01:(P b))=> x01) as proof of (P b)
% 110.80/111.09 Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% 110.80/111.09 Found x01:(P (f0 (f1 (f1 (f1 (f2 x))))))
% 110.80/111.09 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 x))))))
% 110.80/111.09 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P0 ((P (f0 (f1 (f1 (f1 (f2 x))))))->(P (f0 (f1 (f1 (f1 (f2 x))))))))
% 110.80/111.09 Found x01:(P0 (f0 (f1 (f1 (f1 (f2 x))))))
% 110.80/111.09 Found (fun (x01:(P0 (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 x))))))
% 110.80/111.09 Found (fun (P0:(Prop->Prop)) (x01:(P0 (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of ((P0 (f0 (f1 (f1 (f1 (f2 x))))))->(P0 (f0 (f1 (f1 (f1 (f2 x)))))))
% 110.80/111.09 Found (fun (P0:(Prop->Prop)) (x01:(P0 (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P (forall (P0:(Prop->Prop)), ((P0 (f0 (f1 (f1 (f1 (f2 x))))))->(P0 (f0 (f1 (f1 (f1 (f2 x)))))))))
% 110.80/111.09 Found x01:(P (f0 (f1 (f1 (f1 (f2 x))))))
% 110.80/111.09 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 x))))))
% 110.80/111.09 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 x)))))
% 110.80/111.09 Found x01:(P (f0 (f1 (f1 (f1 (f2 x))))))
% 110.80/111.09 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 x))))))
% 110.80/111.09 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 x))))))
% 113.09/113.32 Found x01:(P (f0 (f1 (f1 (f1 (f2 x))))))
% 113.09/113.32 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 x))))))
% 113.09/113.32 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 x)))))))
% 113.09/113.32 Found x01:(P (f0 (f1 (f1 (f1 (f2 x))))))
% 113.09/113.32 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 x))))))
% 113.09/113.32 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 x)))))))
% 113.09/113.32 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 113.09/113.32 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 113.09/113.32 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 113.09/113.32 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 113.09/113.32 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 113.09/113.32 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 113.09/113.32 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 113.09/113.32 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 113.09/113.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 113.09/113.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 113.09/113.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 113.09/113.32 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 113.09/113.32 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 113.09/113.32 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 113.09/113.32 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 113.09/113.32 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 113.09/113.32 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 113.09/113.32 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 113.09/113.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 113.09/113.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 113.09/113.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 113.09/113.32 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 113.09/113.32 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 113.09/113.32 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 113.09/113.32 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 113.09/113.32 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 113.09/113.32 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 113.09/113.32 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 113.09/113.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 113.09/113.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 113.09/113.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 113.09/113.32 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 113.09/113.32 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 113.09/113.32 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 113.09/113.32 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 113.09/113.32 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 113.09/113.32 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 113.09/113.32 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 113.09/113.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 113.09/113.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 114.14/114.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 114.14/114.37 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 114.14/114.37 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 114.14/114.37 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 114.14/114.37 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 114.14/114.37 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 114.14/114.37 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 114.14/114.37 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 114.14/114.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 114.14/114.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 114.14/114.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 114.14/114.37 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 114.14/114.37 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 114.14/114.37 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 114.14/114.37 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 114.14/114.37 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 114.14/114.37 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 114.14/114.37 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 114.14/114.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 114.14/114.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 114.14/114.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 114.14/114.37 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 114.14/114.37 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 114.14/114.37 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 114.14/114.37 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 114.14/114.37 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 114.14/114.37 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 114.14/114.37 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 114.14/114.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 114.14/114.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 114.14/114.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 114.14/114.37 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 114.14/114.37 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 114.14/114.37 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 114.14/114.37 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 114.14/114.37 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 114.14/114.37 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 114.14/114.37 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 114.14/114.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 114.14/114.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 114.14/114.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 114.14/114.37 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 114.14/114.37 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 114.14/114.37 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 117.16/117.46 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 117.16/117.46 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 117.16/117.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 117.16/117.46 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 117.16/117.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 117.16/117.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 117.16/117.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 117.16/117.46 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 117.16/117.46 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 117.16/117.46 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 117.16/117.46 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 117.16/117.46 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 117.16/117.46 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 117.16/117.46 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 117.16/117.46 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 117.16/117.46 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 117.16/117.46 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 117.16/117.46 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 x)))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) (f0 (f1 (f1 (f1 (f2 x))))))
% 117.16/117.46 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b0)
% 117.16/117.46 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b0)
% 117.16/117.46 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b0)
% 117.16/117.46 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b0)
% 117.16/117.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 117.16/117.46 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 117.16/117.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 117.16/117.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 117.16/117.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 117.16/117.46 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 117.16/117.46 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 117.16/117.46 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 117.16/117.46 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 117.16/117.46 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 117.16/117.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 117.16/117.46 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 117.16/117.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 117.16/117.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 117.16/117.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 117.16/117.46 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 117.16/117.46 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 117.16/117.46 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 117.16/117.46 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 117.16/117.46 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 117.16/117.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 117.16/117.46 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 117.16/117.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 117.16/117.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 118.36/118.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 118.36/118.68 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 118.36/118.68 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 118.36/118.68 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 118.36/118.68 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 118.36/118.68 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 118.36/118.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 118.36/118.68 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 118.36/118.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 118.36/118.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 118.36/118.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 118.36/118.68 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 118.36/118.68 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 118.36/118.68 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 118.36/118.68 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 118.36/118.68 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 118.36/118.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 118.36/118.68 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 118.36/118.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 118.36/118.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 118.36/118.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 118.36/118.68 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 118.36/118.68 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 118.36/118.68 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 118.36/118.68 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 118.36/118.68 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 118.36/118.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 118.36/118.68 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 118.36/118.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 118.36/118.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 118.36/118.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 118.36/118.68 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 118.36/118.68 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 118.36/118.68 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 118.36/118.68 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 118.36/118.68 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 118.36/118.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 118.36/118.68 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 118.36/118.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 118.36/118.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 118.36/118.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 118.36/118.68 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 118.36/118.68 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 118.36/118.68 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 121.10/121.34 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 121.10/121.34 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 121.10/121.34 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 121.10/121.34 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 121.10/121.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 121.10/121.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 121.10/121.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 121.10/121.34 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 121.10/121.34 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 121.10/121.34 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 121.10/121.34 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 121.10/121.34 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 121.10/121.34 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 121.10/121.34 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 121.10/121.34 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 121.10/121.34 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 121.10/121.34 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 121.10/121.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 121.10/121.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 121.10/121.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 121.10/121.34 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 121.10/121.34 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 121.10/121.34 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 121.10/121.34 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 121.10/121.34 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 121.10/121.34 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 121.10/121.34 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 121.10/121.34 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P0 (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))
% 121.10/121.34 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 121.10/121.34 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 121.10/121.34 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 121.10/121.34 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 121.10/121.34 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 121.10/121.34 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 121.10/121.34 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 121.10/121.34 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 121.10/121.34 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 121.10/121.34 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 121.10/121.34 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 121.10/121.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 121.10/121.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 121.10/121.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 121.10/121.34 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 121.10/121.34 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 121.10/121.34 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 129.76/130.02 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 129.76/130.02 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 129.76/130.02 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 129.76/130.02 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 129.76/130.02 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 129.76/130.02 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 129.76/130.02 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 129.76/130.02 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 129.76/130.02 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 129.76/130.02 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 129.76/130.02 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 129.76/130.02 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 129.76/130.02 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 129.76/130.02 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 129.76/130.02 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 129.76/130.02 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 129.76/130.02 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 129.76/130.02 Found x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 129.76/130.02 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 129.76/130.02 Found (fun (x01:(P1 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P2 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 129.76/130.02 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 129.76/130.02 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 129.76/130.02 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 129.76/130.02 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 129.76/130.02 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 129.76/130.02 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 129.76/130.02 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 129.76/130.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 129.76/130.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 129.76/130.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 129.76/130.02 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 129.76/130.02 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 129.76/130.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 129.76/130.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 129.76/130.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f1 (f1 (f1 (f2 x))))))
% 129.76/130.02 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 129.76/130.02 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 129.76/130.02 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 129.76/130.02 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 129.76/130.02 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) b)
% 129.76/130.02 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 129.76/130.02 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 129.76/130.02 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 145.06/145.31 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 145.06/145.31 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 145.06/145.31 Found x0:(P0 b)
% 145.06/145.31 Instantiate: b:=(f0 (f0 (f1 (f2 (f2 (f2 x)))))):Prop
% 145.06/145.31 Found (fun (x0:(P0 b))=> x0) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 145.06/145.31 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 145.06/145.31 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 145.06/145.31 Found x0:(P (f1 (f1 (f1 (f2 x)))))
% 145.06/145.31 Instantiate: b:=(f1 (f1 (f1 (f2 x)))):Prop
% 145.06/145.31 Found x0 as proof of (P0 b)
% 145.06/145.31 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 145.06/145.31 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 145.06/145.31 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 145.06/145.31 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 145.06/145.31 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 145.06/145.31 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 145.06/145.31 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f2 x))))
% 145.06/145.31 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 x))))
% 145.06/145.31 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 x))))
% 145.06/145.31 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 x))))
% 145.06/145.31 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 145.06/145.31 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 145.06/145.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 145.06/145.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 145.06/145.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 145.06/145.31 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 145.06/145.31 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 145.06/145.31 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 145.06/145.31 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 145.06/145.31 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 145.06/145.31 Found x02:(P (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 145.06/145.31 Found (fun (x02:(P (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x02) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 145.06/145.31 Found (fun (x02:(P (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x02) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 145.06/145.31 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 145.06/145.31 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f2 x))))
% 145.06/145.31 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 x))))
% 145.06/145.31 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 x))))
% 145.06/145.31 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 x))))
% 145.06/145.31 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 145.06/145.31 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f2 x))))
% 145.06/145.31 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 x))))
% 145.06/145.31 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 x))))
% 145.06/145.31 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 x))))
% 145.06/145.31 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 145.06/145.31 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f2 x))))
% 145.06/145.31 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 x))))
% 145.06/145.31 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 x))))
% 145.06/145.31 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 x))))
% 145.06/145.31 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 145.06/145.31 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 145.06/145.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 145.06/145.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 145.06/145.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 145.06/145.31 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 169.96/170.25 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 169.96/170.25 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 169.96/170.25 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 169.96/170.25 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 169.96/170.25 Found x02:(P (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 169.96/170.25 Found (fun (x02:(P (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x02) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 169.96/170.25 Found (fun (x02:(P (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x02) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 169.96/170.25 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 169.96/170.25 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f2 x))))
% 169.96/170.25 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 x))))
% 169.96/170.25 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 x))))
% 169.96/170.25 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 x))))
% 169.96/170.25 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 169.96/170.25 Found (eq_ref0 a) as proof of (((eq Prop) a) (f1 (f1 (f2 x))))
% 169.96/170.25 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 x))))
% 169.96/170.25 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 x))))
% 169.96/170.25 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f1 (f1 (f2 x))))
% 169.96/170.25 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 169.96/170.25 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 169.96/170.25 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 169.96/170.25 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 169.96/170.25 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 169.96/170.25 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 169.96/170.25 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b0)
% 169.96/170.25 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b0)
% 169.96/170.25 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b0)
% 169.96/170.25 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b0)
% 169.96/170.25 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 169.96/170.25 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 169.96/170.25 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 169.96/170.25 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 169.96/170.25 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 169.96/170.25 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 169.96/170.25 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b0)
% 169.96/170.25 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b0)
% 169.96/170.25 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b0)
% 169.96/170.25 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b0)
% 169.96/170.25 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 169.96/170.25 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 169.96/170.25 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 169.96/170.25 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 169.96/170.25 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 169.96/170.25 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 169.96/170.25 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 169.96/170.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 169.96/170.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 169.96/170.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 169.96/170.25 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 169.96/170.25 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 189.28/189.58 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 189.28/189.58 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 189.28/189.58 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 189.28/189.58 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 189.28/189.58 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 189.28/189.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 189.28/189.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 189.28/189.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 189.28/189.58 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 189.28/189.58 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f1 (f1 (f1 (f2 x)))))
% 189.28/189.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f1 (f1 (f1 (f2 x)))))
% 189.28/189.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f1 (f1 (f1 (f2 x)))))
% 189.28/189.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f1 (f1 (f1 (f2 x)))))
% 189.28/189.58 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 189.28/189.58 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b0)
% 189.28/189.58 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b0)
% 189.28/189.58 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b0)
% 189.28/189.58 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b0)
% 189.28/189.58 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 189.28/189.58 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 189.28/189.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 189.28/189.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 189.28/189.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 189.28/189.58 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 189.28/189.58 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b0)
% 189.28/189.58 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b0)
% 189.28/189.58 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b0)
% 189.28/189.58 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b0)
% 189.28/189.58 Found x01:(P (f1 (f1 (f1 (f2 x)))))
% 189.28/189.58 Found (fun (x01:(P (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P (f1 (f1 (f1 (f2 x)))))
% 189.28/189.58 Found (fun (x01:(P (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 x)))))
% 189.28/189.58 Found x01:(P (f1 (f1 (f1 (f2 x)))))
% 189.28/189.58 Found (fun (x01:(P (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P (f1 (f1 (f1 (f2 x)))))
% 189.28/189.58 Found (fun (x01:(P (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 x)))))
% 189.28/189.58 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 189.28/189.58 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 189.28/189.58 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P0 ((P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))->(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))))
% 189.28/189.58 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 189.28/189.58 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 189.28/189.58 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P0 ((P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))->(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))))
% 189.28/189.58 Found x01:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 189.28/189.58 Found (fun (x01:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 189.28/189.58 Found (fun (P0:(Prop->Prop)) (x01:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of ((P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))->(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))
% 189.28/189.58 Found (fun (P0:(Prop->Prop)) (x01:(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P (forall (P0:(Prop->Prop)), ((P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))->(P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))))
% 192.84/193.12 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 192.84/193.12 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 192.84/193.12 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 192.84/193.12 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 192.84/193.12 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 192.84/193.12 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 192.84/193.12 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 192.84/193.12 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 192.84/193.12 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 192.84/193.12 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 192.84/193.12 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 192.84/193.12 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 192.84/193.12 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 192.84/193.12 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 192.84/193.12 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P0 (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))
% 192.84/193.12 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 192.84/193.12 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 192.84/193.12 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P0 (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))
% 192.84/193.12 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 192.84/193.12 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 192.84/193.12 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P0 (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))
% 192.84/193.12 Found x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 192.84/193.12 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 192.84/193.12 Found (fun (x01:(P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x01) as proof of (P0 (P (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))
% 192.84/193.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 192.84/193.12 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 192.84/193.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 192.84/193.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 192.84/193.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 192.84/193.12 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 192.84/193.12 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 192.84/193.12 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 192.84/193.12 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 192.84/193.12 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 192.84/193.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 192.84/193.12 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 192.84/193.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 192.84/193.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 192.84/193.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 192.84/193.12 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 192.84/193.12 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 192.84/193.12 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 192.84/193.12 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 192.84/193.12 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 204.54/204.82 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 204.54/204.82 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 204.54/204.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 204.54/204.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 204.54/204.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 204.54/204.82 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 204.54/204.82 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 204.54/204.82 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 204.54/204.82 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 204.54/204.82 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 204.54/204.82 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 204.54/204.82 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 204.54/204.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 204.54/204.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 204.54/204.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 204.54/204.82 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 204.54/204.82 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 204.54/204.82 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 204.54/204.82 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 204.54/204.82 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 204.54/204.82 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 204.54/204.82 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 204.54/204.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 204.54/204.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 204.54/204.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 204.54/204.82 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 204.54/204.82 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 204.54/204.82 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 204.54/204.82 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 204.54/204.82 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 204.54/204.82 Found x01:(P (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 204.54/204.82 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 204.54/204.82 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 204.54/204.82 Found x0:(P (f1 (f1 (f1 (f2 x)))))
% 204.54/204.82 Instantiate: b:=(f1 (f1 (f1 (f2 x)))):Prop
% 204.54/204.82 Found x0 as proof of (P0 b)
% 204.54/204.82 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 204.54/204.82 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 204.54/204.82 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 204.54/204.82 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 204.54/204.82 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 204.54/204.82 Found x01:(P (f0 (f1 (f1 (f1 (f2 x))))))
% 204.54/204.82 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 x))))))
% 204.54/204.82 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P0 (f0 (f1 (f1 (f1 (f2 x))))))
% 204.54/204.82 Found x01:(P (f0 (f1 (f1 (f1 (f2 x))))))
% 204.54/204.82 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P (f0 (f1 (f1 (f1 (f2 x))))))
% 204.54/204.82 Found (fun (x01:(P (f0 (f1 (f1 (f1 (f2 x)))))))=> x01) as proof of (P0 (P (f0 (f1 (f1 (f1 (f2 x)))))))
% 204.54/204.82 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 204.54/204.82 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 206.66/206.95 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 206.66/206.95 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 206.66/206.95 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 206.66/206.95 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 206.66/206.95 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 206.66/206.95 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 206.66/206.95 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 206.66/206.95 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 206.66/206.95 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 206.66/206.95 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 206.66/206.95 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 206.66/206.95 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 206.66/206.95 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 206.66/206.95 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 206.66/206.95 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 206.66/206.95 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 206.66/206.95 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 206.66/206.95 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 206.66/206.95 Found x01:(P (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 206.66/206.95 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 206.66/206.95 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 206.66/206.95 Found eq_ref00:=(eq_ref0 (f0 (f1 (f1 (f1 (f2 x)))))):(((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) (f0 (f1 (f1 (f1 (f2 x))))))
% 206.66/206.95 Found (eq_ref0 (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b)
% 206.66/206.95 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b)
% 206.66/206.95 Found ((eq_ref Prop) (f0 (f1 (f1 (f1 (f2 x)))))) as proof of (((eq Prop) (f0 (f1 (f1 (f1 (f2 x)))))) b)
% 206.66/206.95 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 206.66/206.95 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 206.66/206.95 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 206.66/206.95 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 206.66/206.95 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 206.66/206.95 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 206.66/206.95 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 206.66/206.95 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 206.66/206.95 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 206.66/206.95 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 206.66/206.95 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 206.66/206.95 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 206.66/206.95 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 206.66/206.95 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 206.66/206.95 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 206.66/206.95 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 206.66/206.95 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 206.66/206.95 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 206.66/206.95 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 206.66/206.95 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 206.66/206.95 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 206.66/206.95 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 207.54/207.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 207.54/207.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 207.54/207.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 207.54/207.86 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 207.54/207.86 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 207.54/207.86 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 207.54/207.86 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 207.54/207.86 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 207.54/207.86 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 207.54/207.86 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 207.54/207.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 207.54/207.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 207.54/207.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 207.54/207.86 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 207.54/207.86 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 207.54/207.86 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 207.54/207.86 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 207.54/207.86 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 207.54/207.86 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 207.54/207.86 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 207.54/207.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 207.54/207.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 207.54/207.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 207.54/207.86 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 207.54/207.86 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 207.54/207.86 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 207.54/207.86 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 207.54/207.86 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 207.54/207.86 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 207.54/207.86 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 207.54/207.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 207.54/207.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 207.54/207.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 207.54/207.86 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 207.54/207.86 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 207.54/207.86 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 207.54/207.86 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 207.54/207.86 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 207.54/207.86 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 207.54/207.86 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 207.54/207.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 207.54/207.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 207.54/207.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 207.54/207.86 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 207.54/207.86 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 207.54/207.86 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 207.54/207.86 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 207.54/207.86 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 234.23/234.57 Found x01:(P (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 234.23/234.57 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 234.23/234.57 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 234.23/234.57 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 234.23/234.57 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (P1 (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))
% 234.23/234.57 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (P1 (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))
% 234.23/234.57 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (P1 (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))
% 234.23/234.57 Found eq_ref00:=(eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))):(((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 234.23/234.57 Found (eq_ref0 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (P1 (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))
% 234.23/234.57 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (P1 (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))
% 234.23/234.57 Found ((eq_ref Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) as proof of (P1 (((eq Prop) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))) (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))
% 234.23/234.57 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 234.23/234.57 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 234.23/234.57 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 234.23/234.57 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 234.23/234.57 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 234.23/234.57 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 234.23/234.57 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 234.23/234.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 234.23/234.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 234.23/234.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 234.23/234.57 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 234.23/234.57 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 234.23/234.57 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 234.23/234.57 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 234.23/234.57 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 234.23/234.57 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 234.23/234.57 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 234.23/234.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 234.23/234.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 234.23/234.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 234.23/234.57 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 234.23/234.57 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 234.23/234.57 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 234.23/234.57 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 234.23/234.57 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 234.23/234.57 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 234.23/234.57 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 234.23/234.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 234.23/234.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 234.23/234.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 261.71/262.06 Found x02:(P (f1 (f1 (f1 (f2 x)))))
% 261.71/262.06 Found (fun (x02:(P (f1 (f1 (f1 (f2 x))))))=> x02) as proof of (P (f1 (f1 (f1 (f2 x)))))
% 261.71/262.06 Found (fun (x02:(P (f1 (f1 (f1 (f2 x))))))=> x02) as proof of (P0 (f1 (f1 (f1 (f2 x)))))
% 261.71/262.06 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 261.71/262.06 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 261.71/262.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 261.71/262.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 261.71/262.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 261.71/262.06 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 261.71/262.06 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 261.71/262.06 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 261.71/262.06 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 261.71/262.06 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 261.71/262.06 Found x01:(P0 (f1 (f1 (f1 (f2 x)))))
% 261.71/262.06 Found (fun (x01:(P0 (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 x)))))
% 261.71/262.06 Found (fun (x01:(P0 (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 x)))))
% 261.71/262.06 Found x01:(P0 (f1 (f1 (f1 (f2 x)))))
% 261.71/262.06 Found (fun (x01:(P0 (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P0 (f1 (f1 (f1 (f2 x)))))
% 261.71/262.06 Found (fun (x01:(P0 (f1 (f1 (f1 (f2 x))))))=> x01) as proof of (P1 (f1 (f1 (f1 (f2 x)))))
% 261.71/262.06 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 261.71/262.06 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 261.71/262.06 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 261.71/262.06 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 261.71/262.06 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 261.71/262.06 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 261.71/262.06 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b0)
% 261.71/262.06 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b0)
% 261.71/262.06 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b0)
% 261.71/262.06 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b0)
% 261.71/262.06 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 261.71/262.06 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 261.71/262.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 261.71/262.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 261.71/262.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 261.71/262.06 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 261.71/262.06 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 261.71/262.06 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 261.71/262.06 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 261.71/262.06 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 261.71/262.06 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 261.71/262.06 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 261.71/262.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 261.71/262.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 261.71/262.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 261.71/262.06 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 261.71/262.06 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 261.71/262.06 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 261.71/262.06 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 261.71/262.06 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 267.19/267.50 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 267.19/267.50 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 267.19/267.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 267.19/267.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 267.19/267.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 267.19/267.50 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 267.19/267.50 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 267.19/267.50 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 267.19/267.50 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 267.19/267.50 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 267.19/267.50 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 267.19/267.50 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 267.19/267.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 267.19/267.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 267.19/267.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 267.19/267.50 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 267.19/267.50 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 267.19/267.50 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 267.19/267.50 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 267.19/267.50 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 267.19/267.50 Found x01:(P (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 267.19/267.50 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 267.19/267.50 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 267.19/267.50 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 267.19/267.50 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 267.19/267.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 267.19/267.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 267.19/267.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 267.19/267.50 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 267.19/267.50 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 267.19/267.50 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 267.19/267.50 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 267.19/267.50 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 267.19/267.50 Found x0:(P2 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 267.19/267.50 Found (fun (x0:(P2 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x0) as proof of (P2 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 267.19/267.50 Found (fun (P2:(Prop->Prop)) (x0:(P2 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x0) as proof of ((P2 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))->(P2 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))
% 267.19/267.50 Found (fun (P2:(Prop->Prop)) (x0:(P2 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x0) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 267.19/267.50 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 267.19/267.50 Found (eq_ref0 b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 267.19/267.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 267.19/267.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 267.19/267.50 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f1 (f1 (f1 (f2 x)))))
% 267.19/267.50 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 267.19/267.50 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 275.02/275.37 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 275.02/275.37 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 275.02/275.37 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 275.02/275.37 Found x0:(P2 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 275.02/275.37 Found (fun (x0:(P2 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x0) as proof of (P2 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))
% 275.02/275.37 Found (fun (P2:(Prop->Prop)) (x0:(P2 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x0) as proof of ((P2 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))))->(P2 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))
% 275.02/275.37 Found (fun (P2:(Prop->Prop)) (x0:(P2 (f0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))))=> x0) as proof of (P1 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 275.02/275.37 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 275.02/275.37 Found (eq_ref0 a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 x))))))
% 275.02/275.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 x))))))
% 275.02/275.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 x))))))
% 275.02/275.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 x))))))
% 275.02/275.37 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 275.02/275.37 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b0)
% 275.02/275.37 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b0)
% 275.02/275.37 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b0)
% 275.02/275.37 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b0)
% 275.02/275.37 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 275.02/275.37 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 275.02/275.37 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 275.02/275.37 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 275.02/275.37 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 275.02/275.37 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 275.02/275.37 Found (eq_ref0 a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 x))))))
% 275.02/275.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 x))))))
% 275.02/275.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 x))))))
% 275.02/275.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 x))))))
% 275.02/275.37 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 275.02/275.37 Found (eq_ref0 a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 x))))))
% 275.02/275.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 x))))))
% 275.02/275.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 x))))))
% 275.02/275.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f0 (f1 (f2 (f2 (f2 x))))))
% 275.02/275.37 Found x01:(P (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 275.02/275.37 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 275.02/275.37 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 275.02/275.37 Found x01:(P (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 275.02/275.37 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 275.02/275.37 Found (fun (x01:(P (f0 (f0 (f1 (f2 (f2 (f2 x))))))))=> x01) as proof of (P0 (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 275.02/275.37 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 275.02/275.37 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b0)
% 275.02/275.37 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b0)
% 275.02/275.37 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b0)
% 275.02/275.37 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b0)
% 275.02/275.37 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 275.02/275.37 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 275.02/275.37 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 275.02/275.37 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 288.27/288.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 288.27/288.66 Found x02:(P (f1 (f1 (f1 (f2 x)))))
% 288.27/288.66 Found (fun (x02:(P (f1 (f1 (f1 (f2 x))))))=> x02) as proof of (P (f1 (f1 (f1 (f2 x)))))
% 288.27/288.66 Found (fun (x02:(P (f1 (f1 (f1 (f2 x))))))=> x02) as proof of (P0 (f1 (f1 (f1 (f2 x)))))
% 288.27/288.66 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 288.27/288.66 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 288.27/288.66 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 288.27/288.66 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 288.27/288.66 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 288.27/288.66 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 288.27/288.66 Found (eq_ref0 b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 288.27/288.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 288.27/288.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 288.27/288.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 288.27/288.66 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 288.27/288.66 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 288.27/288.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 288.27/288.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 288.27/288.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 288.27/288.66 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 288.27/288.66 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 288.27/288.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 288.27/288.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 288.27/288.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 288.27/288.66 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 288.27/288.66 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 288.27/288.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 288.27/288.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 288.27/288.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 288.27/288.66 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 288.27/288.66 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 288.27/288.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 288.27/288.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 288.27/288.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 288.27/288.66 Found x0:(P (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 288.27/288.66 Instantiate: b:=(f0 (f0 (f1 (f2 (f2 (f2 x)))))):Prop
% 288.27/288.66 Found x0 as proof of (P0 b)
% 288.27/288.66 Found eq_ref00:=(eq_ref0 (f1 (f1 (f1 (f2 x))))):(((eq Prop) (f1 (f1 (f1 (f2 x))))) (f1 (f1 (f1 (f2 x)))))
% 288.27/288.66 Found (eq_ref0 (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 288.27/288.66 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 288.27/288.66 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 288.27/288.66 Found ((eq_ref Prop) (f1 (f1 (f1 (f2 x))))) as proof of (((eq Prop) (f1 (f1 (f1 (f2 x))))) b)
% 288.27/288.66 Found eq_ref00:=(eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))):(((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 288.27/288.66 Found (eq_ref0 (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 288.27/288.66 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 288.27/288.66 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 288.27/288.66 Found ((eq_ref Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) as proof of (((eq Prop) (f0 (f0 (f1 (f2 (f2 (f2 x))))))) b)
% 288.27/288.66 Found x0:(P0 b)
% 288.27/288.66 Instantiate: b:=(f1 (f1 (f1 (f2 x)))):Prop
% 288.27/288.66 Found (fun (x0:(P0 b))=> x0) as proof of (P0 (f1 (f1 (f1 (f2 x)))))
% 288.27/288.66 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (f1 (f1 (f1 (f2 x))))))
% 288.27/288.66 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 288.27/288.66 Found x0:(P (f0 (f0 (f1 (f2 (f2 (f2 x)))))))
% 288.27/288.66 Instantiate: b:=(f0 (f0 (f1 (f2 (f2 (f2 x)))))):Prop
% 288.27/288.66 Found x0 as proof of (P0 b)
% 288.27/288.66 Found eq_ref00:=(eq_ref0 (f1 (f
%------------------------------------------------------------------------------